(2x+11)(2x+4)=120

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Solution for (2x+11)(2x+4)=120 equation: 


Simplifying
(2x + 11)(2x + 4) = 120

Reorder the terms:
(11 + 2x)(2x + 4) = 120

Reorder the terms:
(11 + 2x)(4 + 2x) = 120

Multiply (11 + 2x) * (4 + 2x)
(11(4 + 2x) + 2x * (4 + 2x)) = 120
((4 * 11 + 2x * 11) + 2x * (4 + 2x)) = 120
((44 + 22x) + 2x * (4 + 2x)) = 120
(44 + 22x + (4 * 2x + 2x * 2x)) = 120
(44 + 22x + (8x + 4x2)) = 120

Combine like terms: 22x + 8x = 30x
(44 + 30x + 4x2) = 120

Solving
44 + 30x + 4x2 = 120

Solving for variable 'x'.

Reorder the terms:
44 + -120 + 30x + 4x2 = 120 + -120

Combine like terms: 44 + -120 = -76
-76 + 30x + 4x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-76 + 30x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-38 + 15x + 2x2) = 0

Factor a trinomial.
2((-19 + -2x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-19 + -2x)' equal to zero and attempt to solve:

Simplifying
-19 + -2x = 0

Solving
-19 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '19' to each side of the equation.
-19 + 19 + -2x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2x = 0 + 19
-2x = 0 + 19

Combine like terms: 0 + 19 = 19
-2x = 19

Divide each side by '-2'.
x = -9.5

Simplifying
x = -9.5

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-9.5, 2}

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